Guided Backprop

What it does?

Guided backpropagation is a variant of saliency that changes how the signal flows backward through the network. At each rectifier it keeps only the positive contributions and zeroes the negative ones, on both the forward activation and the backward gradient. The effect is a much sharper, cleaner-looking saliency map, which is why the method became popular for visualising what a network 'sees'. The intuition is that suppressing the negative evidence isolates the features that positively drive the output. We apply the same rectified-backward rule to the VCS and correlate the resulting map with the true causal map. A well-known concern, raised by Adebayo and colleagues, is that guided backprop can act more like an edge detector than a true explanation, producing similar maps even when the model is randomised. We run exactly that sanity check on the machine itself. On smooth content outputs the method partly tracks the true cause. On a sprite's position it hits the gradient wall: the position is a discrete strobe-timed step, so the underlying gradient is zero, and the rectified backward path leaves it at zero here rather than restoring any signal. Combined with its failure of the randomisation check, this makes guided backprop a revealing case: it looks sharp and convincing yet does not depend on what the program actually computes.

Top row (image domain, as in Paper 1): the game frame, then the oracle's true causal region and this method's attributed region — each painted onto the frame through the screen footprint of the RAM cells it implicates (brighter = more important). A faithful method's heat matches the oracle's. Bottom: per-cell importance — oracle (green) vs method (blue) — and the deletion/insertion faithfulness curves (perturb the ranked causes and watch the output move). Note: the image-domain overlay footprints are illustrative, computed on the pre-redesign boot frame; the bars, curves and all reported numbers come from the re-run records on the shared gameplay states. pearson_corr_with_oracle = 0.464 — this example only (pong, state f90+15); the audit aggregate is below.

Reading this example's causal region

This example explains the content of RAM $36 (byte 54) — the most causally-active concept byte at this state. Its strongest true-causes are: RAM $36 (the play area — ball / paddles); RAM $31 (17% of its footprint sits in the score band, the rest in the play area). The score digits appear in the region because RAM $31 reaches them: perturbing it over the 30-frame NOOP window changes the game outcome, and hence the score — a downstream effect, not direct rendering.

How it's scored

The score is the Pearson correlation of the guided-backprop map with the oracle's exact causal map, reported raw, and the grading is always against the intervention oracle. On smooth content outputs the rectified backward pass partly tracks the true cause. The hard case is a sprite's position: it is a discrete strobe-timed step, so the naive gradient is provably zero, and here the method's rectified path leaves it at zero rather than restoring any signal. On top of that, guided backprop fails the Adebayo program-randomisation sanity check on the machine itself. We scramble the ROM so the program boots to a completely different state, and the content-path map stays essentially unchanged, because its Jacobian is a constant one-hot pointing at the read index, independent of what the program computes. A faithful explanation must change when the model changes; this one does not. So even where it looks sharp, it is model-invariant, which the intervention oracle exposes at once by distinguishing the two programs. Between the zero position gradient and the failed sanity check, its cross-game faithfulness stays low. The audit box reports the measured all-regime faithfulness across the scored games.

The score is measured against the §1 intervention oracle — never against another interpretability method. F (faithful) is always vs the oracle; see the execution stack. How each of F / S / M is actually computed for this method (and whether it matches the paper) is in the box just below; the numbers are in the In the audit box under it.

How F, S, M are computed here

The exact formula this method uses for each score, read from its runner, and whether it matches the paper's §3 (F ∧ S ∧ M triad) definition. From the committed audit fsm_math_phaseB.json.

Axis	Formula (as computed)	What it measures	Matches §3?
F faithfulness	\(F = \rho_{\mathrm{Pearson}}\!\left(\mathrm{attr},\ |\Delta y(u)|\right)\)	Raw Pearson correlation between the method's per-cause attribution magnitudes and the oracle's true absolute causal effects |Delta_y(u)|, scored separately for the content and position output regimes.	✓ matches guided_backprop.jl: attr = guided-backprop per cause, F = pearson(attr, oracle_abs_delta); triad_extra_dict(f.pearson, attr, f.oracle_abs_delta). Record: out/guided_backprop_air_raid_content.json (metric_name=pearson_corr_with_oracle, value=0.79). Scorer pilot_ig_vs_oracle.jl pearson() (raw Statistics.cor, zero-variance->0); F = pearson(attr, oracle_abs_delta) where oracle_abs_delta = abs.(cmap.delta) (true |Delta_y| per cause). Also reports spearman, precision@k, deletion/insertion AUC (paper's auxiliary F metrics). Per-regime split: separate *_content.json and *_position.json records, each carrying its own extra.triad.{F,S,M}. how it's measured — call stack: per-cause guided-backprop attribution — guided_backprop.jl:601 raw Pearson of attribution vs oracle |Δy(u)| — pilot_ig_vs_oracle.jl:173 assemble the F∧S∧M triad record — guided_backprop.jl:909 true causal effect Δy(u) by bit-exact re-run — oracle_intervene.jl:242
S sufficiency	\(S = \dfrac{\#\{\,u_{\mathrm{held}}:\ |\hat{y}-y|\le\varepsilon\,\}}{|\mathrm{held\text{-}out}|}\in[0,1]\)	Fit Delta_y = a*attr + b on a calibration half of the do(u) causes, predict the disjoint held-out half, and report the fraction of held-out causes whose predicted output lands within an epsilon band of the oracle's bit-exact re-run.	✓ matches common/triad_sm.jl sufficiency_score() (interleaved calib/held split by seed, least-squares 1-D fit Delta_y~a*attr+b on calib, epsilon = max(0.5, 0.10*heldout_spread)); assembled in triad_extra_dict(). The new §3 (sec:triad) admits the fraction-within-tolerance [0,1] special case of the held-out predictive test, which this held-out do(u) fit-then-predict estimator satisfies, so it matches. (Detail: epsilon is a self-scaled band 0.10*spread; the [-1,1] correlation form is available but this method reports the [0,1] hit fraction.) how it's measured — call stack: sufficiency_score: fit Δy=a·attr+b on a calib half, predict held-out within ε — triad_sm.jl:111 assemble the F∧S∧M triad record (calls sufficiency_score) — triad_sm.jl:173 true causal effect Δy(u) by bit-exact re-run — oracle_intervene.jl:242
M minimality	\(M = |U^{\star}| / |\hat{U}| \in (0,1]\quad U^{\star}=\{u:\Delta y(u)>0\},\ \hat{U}=\{u:|\mathrm{attr}(u)|>\tau\}\)	Ratio of the number of oracle causal movers (causes with nonzero true Delta_y) to the number of cells the method names above 1e-6 of its own max attribution; null when the oracle finds no mover or the method names nothing.	✓ matches common/triad_sm.jl minimality_score() with name_frac=1e-6, mover_floor=0.0; the above-threshold named set is used (topk kept but not passed), see triad_extra_dict(). This is the paper's M = |U*|/|U_hat| in (0,1] (standardized everywhere), so it matches the new §3. (Detail: |U*| is taken as all oracle movers with Delta_y>0, an upper bound on the strictly-smallest reproducing subset, so M can be optimistic.) how it's measured — call stack: minimality_score: |U*| oracle movers / |U_hat| named cells — triad_sm.jl:57 assemble the triad record (calls minimality_score) — triad_sm.jl:178 true causal effect Δy(u) by bit-exact re-run — oracle_intervene.jl:242

✓ matches = the same quantity as §3; ◐ partial = the same kind of estimator but a differing detail; ✗ does not match = a different quantity (see the note). Definitions: F = agreement with the oracle's true causal effects Δy(u); S = held-out predictive score in [−1, 1]; M = |U*|/|Û| (true-minimal-set size / named-set size).

In the audit

This is the method's entry in the actual cross-method audit — scored on the paper's correctness triad, each axis a mean over all 42 scored games (84 committed §R records), not the single example shown above. Tradition: gradient. The example figure (Pong) is one of those records.

F faithfulness (scored vs the oracle for every method) · S sufficiency (held-out predictive score in [−1, 1]; a negative value means the explanation predicts held-out interventions worse than the unperturbed baseline; reported for the predictive methods across all three phases where the calibration/held-out split is defined) · M minimality (true-minimal-set / named-set; where the method names a cause set) — n/a otherwise, per the paper's F ∧ S ∧ M triad.

Source: leaderboard.json · the whole leaderboard is on the methods page and the Paper 2 audit.

Results per game

This method's faithfulness on each of the 42 scored games (all-regime F, and the content vs position split). Click a header to sort. Every number is read from site_data.json (methods.guided_backprop.per_game).

Game	F (all)	content-F	position-F	S	M	Note
Space Invaders	0.500	1.000	0.000	0.556	1.000	position gradient vanishes
Tennis	0.500	1.000	0.000	0.500	1.000	position gradient vanishes
Montezuma's Revenge	0.500	1.000	0.000	0.938	1.000	position gradient vanishes
Riverraid	0.500	1.000	0.000	0.500	1.000	position gradient vanishes
Kangaroo	0.500	0.999	0.000	0.500	1.000	position gradient vanishes
Krull	0.500	1.000	0.000	0.500	1.000	position gradient vanishes
Q*bert	0.500	0.999	0.000	0.500	1.000	position gradient vanishes
Demon Attack	0.477	0.955	0.000	0.875	1.000	position gradient vanishes
Fishing Derby	0.474	0.948	0.000	0.450	1.000	position gradient vanishes
Phoenix	0.455	0.909	0.000	0.577	1.000	position gradient vanishes
Bank Heist	0.450	0.900	0.000	0.833	1.000	position gradient vanishes
Boxing	0.408	0.817	0.000	0.500	1.000	position gradient vanishes
Ms. Pac-Man	0.405	0.810	0.000	0.475	1.000	position gradient vanishes
Air Raid	0.395	0.791	0.000	0.464	1.000	position gradient vanishes
Name This Game	0.394	0.788	0.000	0.417	1.000	position gradient vanishes
Alien	0.390	0.779	0.000	0.500	1.000	position gradient vanishes
Pacman	0.388	0.776	0.000	0.556	1.000	position gradient vanishes
Gopher	0.388	0.776	0.000	0.929	1.000	position gradient vanishes
Atlantis	0.386	0.773	0.000	0.400	1.000	position gradient vanishes
Yars' Revenge	0.385	0.771	0.000	0.464	1.000	position gradient vanishes
Video Pinball	0.385	0.770	0.000	0.500	1.000	position gradient vanishes
Ice Hockey	0.384	0.767	0.000	0.500	1.000	position gradient vanishes
Beam Rider	0.383	0.766	0.000	0.417	1.000	position gradient vanishes
Private Eye	0.382	0.764	0.000	0.960	1.000	position gradient vanishes
Breakout	0.375	0.750	0.000	0.550	1.000	position gradient vanishes
Jamesbond	0.374	0.747	0.000	0.893	1.000	position gradient vanishes
Freeway	0.373	0.747	0.000	0.567	1.000	position gradient vanishes
Kung-Fu Master	0.372	0.745	0.000	0.800	1.000	position gradient vanishes
Venture	0.372	0.743	0.000	0.474	1.000	position gradient vanishes
Double Dunk	0.369	0.738	0.000	0.808	1.000	position gradient vanishes
Bowling	0.344	0.688	0.000	0.881	1.000	position gradient vanishes
Frostbite	0.242	0.484	0.000	0.150	1.000	position gradient vanishes
Pong	0.232	0.464	0.000	0.389	1.000	position gradient vanishes
Berzerk	0.048	0.096	0.000	0.481	1.000	position gradient vanishes
Seaquest	0.009	0.017	0.000	0.479	1.000	position gradient vanishes
Assault	0.000	0.000	0.000	0.905	1.000	position gradient vanishes
Carnival	0.000	0.000	0.000	0.500	1.000	position gradient vanishes
Centipede	0.000	0.000	0.000	0.450	1.000	position gradient vanishes
Chopper Command	0.000	0.000	0.000	0.476	0.500	position gradient vanishes
Hero	0.000	0.000	0.000	0.444	0.500	position gradient vanishes
Pitfall	0.000	0.000	0.000	0.882	1.000	position gradient vanishes
Road Runner	0.000	0.000	0.000	0.105	0.500	position gradient vanishes

Call stack — how it runs on jutari / jaxtari

The path from this method's runner (main) into the bit-exact VCS substrate, and the computation it involves. Every step links to the exact source on main. From callstack_phaseB.json.

Applied on the substrate

1. env reset + per-frame step of the bit-exact VCS — env_reset! / env_step! jutari
2. shared gameplay-state testbed — build_shared_testbed jutari

The computation (differentiable / gradient path)

1. CONTENT output = forward-exact one-hot RAM read; a LINEAR unit (dy/du = e_idx >= 0) — content_read -> soft_ram_peek jutari-diff call site tools/xai_study/phaseB_attribution/guided_backprop.jl:320
2. Guided Backprop: gradient then keep positive part (guided_rule) => |positive part|; returns (guided, vanilla) — guided_backprop_over_ram runner
3. autodiff yielding the raw gradient the guided rule rectifies — Zygote.gradient(readf, x) Zygote
4. POSITION path restored via bilinear sampler (shared testbed) — _st_sampler_position_read runner-diff

Scored against the exact intervention oracle Δy(u): run_intervention.

On jaxtari (JAX / GPU): the same differentiable path has a bit-exact JAX sibling (Theorem 1, forward-exact) for batched GPU runs — JAX-equivalent differentiable path (bit-exact per Theorem 1, for GPU batching): jaxtari/jaxtari/diff/soft_step.py, soft_mem.py, straight_through.py

Implementation

tools/xai_study/phaseB_attribution/guided_backprop.jl

Reference

Springenberg et al. 2015

Record

guided_backprop_pong_content.json

All records

phaseB_attribution/out

The figure is generated from the committed record by docs/gen_method_figures.py; the game frame and each RAM cell's screen footprint are produced by render_scenes.jl / cell_footprints.jl.